An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between

130130

lb and

181181

lb. The new population of pilots has normally distributed weights with a mean of

136 lb136lb

and a standard deviation of

25.6 lb25.6lb.

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Part 1

a. If a pilot is randomly selected, find the probability that his weight is between

130130

lb and

181181

lb.

The probability is approximately

0.55330.5533.

(Round to four decimal places as needed.)

Part 2

b. If

3838

different pilots are randomly selected, find the probability that their mean weight is between

130130

lb and

181181

lb.

The probability is approximately

0.92570.9257.

(Round to four decimal places as needed.)

Part 3

c. When redesigning the ejection seat, which probability is more relevant?

A.

Part (b) because the seat performance for a sample of pilots is more important.

B.

Part (a) because the seat performance for a sample of pilots is more important.

C.

Part (a) because the seat performance for a single pilot is more important.

D.

Part (b) because the seat performance for a single pilot is more important.